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-$$
-\def\mod{\mathrel{\big/}}
-\Dg
-{\rm Spin}(3) & & & & SU(2) \\
- & \rdTo & & \ldTo \\
- & & SO(3) \\
- & & \dTo \\
-& O(3)\mod O(1)^3 = {} & SO(3)\mod(O(1)^3\cap SO(3)) \\
-\endDg
-$$